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Properties

Label 1045.4.bo
Level $1045$
Weight $4$
Character orbit 1045.bo
Rep. character $\chi_{1045}(199,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1800$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.bo (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1045, [\chi])\).

Total New Old
Modular forms 2184 1800 384
Cusp forms 2136 1800 336
Eisenstein series 48 0 48

Trace form

\( 1800 q - 36 q^{4} - 36 q^{6} + O(q^{10}) \) \( 1800 q - 36 q^{4} - 36 q^{6} - 18 q^{10} - 396 q^{14} - 12 q^{15} - 972 q^{16} + 864 q^{19} - 576 q^{21} - 660 q^{24} - 192 q^{25} + 96 q^{29} - 798 q^{30} - 2232 q^{31} - 1584 q^{34} + 828 q^{35} + 1296 q^{36} - 1824 q^{39} + 144 q^{40} + 1368 q^{45} + 44100 q^{49} - 2142 q^{50} + 936 q^{51} + 1296 q^{54} + 16128 q^{56} - 1440 q^{59} - 5790 q^{60} - 2592 q^{61} + 54864 q^{64} + 480 q^{65} + 8208 q^{69} - 2148 q^{70} - 11088 q^{71} - 7068 q^{74} + 9912 q^{75} + 576 q^{76} + 18072 q^{79} + 14418 q^{80} + 4224 q^{81} + 2304 q^{84} - 1008 q^{85} + 3600 q^{86} - 4608 q^{89} - 8070 q^{90} - 8688 q^{91} - 12816 q^{94} - 11676 q^{95} - 10944 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1045, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)